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3.5  Adding and subtracting decimals



               3.5 Adding and subtracting decimals


               When you add and subtract decimal numbers mentally, there are different methods you can use.
               t   When you are adding, you can break down the numbers into their whole-number and decimal parts.
                 !en add the whole-number parts, add the decimal parts, and 'nally add the whole-number answer
                 to the decimal answer.
               t   When you are subtracting, you can break down the number you are subtracting into its
                 whole-number part and decimal part. !en subtract the whole-number part 'rst and subtract
                 the decimal part second.
               t   If one of the numbers you are adding or subtracting is close to a whole number, you can round it to
                 the nearest whole number, do the addition or subtraction, then adjust your answer at the end.


               Worked example 3.5A
                Work these out mentally.   a  2.3 + 7.8   b  6.9 + 12.4     c  13.3 − 5.8

                a  2.3 + 7.8 = 2 + 7 + 0.3 + 0.8   Break the numbers into whole-number and decimal parts.
                    = 9 + 1.1                    Add the whole-number parts and add the decimal parts.
                    = 10.1                       Add the whole-number answer to the decimal answer.
                b  6.9 + 12.4 = 7 + 12.4 − 0.1   Round 6.9 up to 7 and subtract 0.1 later.
                    = 19.4 − 0.1                 Add 7 to 12.4.
                    = 19.3                       Subtract 0.1.
                c  13.3 − 5.8 = 13.3 − 6 + 0.2   Round 5.8 up to 6 and add 0.2 later.
                    = 7.3 + 0.2                  Subtract 6 from 13.3.
                    = 7.5                        Add 0.2.



               When you use a written method to add and subtract decimal numbers, always write the calculation in
               columns, with the decimal points vertically in line. !en add and subtract as normal but remember to
               write the decimal point in your answer.


               Worked example 3.5B

                Work these out.   a  27.52 + 4.8   b  43.6 − 5.45

                  a
                       2 7 . 5     2       Start with the hundredths column: 2 + 0 = 2.
                      +   4 . 8            Next add the tenths: 5 + 8 = 13; write down the 3, carry the 1.
                       3 2 . 3     2       Now add the units: 7 + 4 + 1 = 12; write down the 2, carry the 1.
                                           Finally add the tens: 2 + 1 = 3.
                        1  1

                  b     3 4  1 3 .  5 6  1 0  First write 43.6 as 43.60.
                     −     5 . 4    5      Start by subtracting in the hundredths column: you can’t take 5 from 0
                                           (0 − 5), so borrow from the 6 tenths, then work out 10 − 5 = 5.
                        3  8 .   1  5
                                           Now subtract the tenths: 5 − 4 = 1.
                                           Now the units: you can’t take 5 from 3 (3 − 5), so borrow from the 4
                                           tens, then work out 13 − 5 = 8.
                                           Finally the tens: 3 − 0 = 3.



       38      3 Place value, ordering and rounding
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